Conventionally, a 2m QAM (m is a positive integer) modulation and demodulation scheme, such as 64 QAM, 128 QAM, or 256 QAM, has been used in various communication system such as a digital microwave communication system. In the 2m QAM modulation and demodulation scheme, communication is performed through a bit mapping procedure in which 2m m-bit data patterns in total are assigned to 2m signal points.
In order to protect data from noise to be generated in the communication, an error correction code which is redundant data to be added to the communication data to increase error resistance is added. The application of the error correction code generally significantly improves error rate. However, it is known that an effect of the error correction coding differs depending on how to combine the error correction code with the signal point mapping (see, for example, NPLs 1 and 2). In particular, by changing distribution of the redundant bits of the error correction code in consideration of a relationship between a distance among the signal points and a Hamming distance among the m-bit data patterns mapped to respective signal points, the effect of the error correction coding can be increased. This also makes it possible, in a bandwidth-limited communication channel, to suppress band expansion due to the addition of the redundant bits without degrading the error rate.
Hereinafter, to differentiate between the distance among the signal points and the Hamming distance which is the distance among the bit sequences, the former is referred to as “Euclidean distance”.
FIGS. 1 and 2 each illustrate an example of a related art in which the error correction code such as a Reed-Solomon code (RS code) or a low-density parity-check code (LDPC code) is applied to a 16 QAM modulation scheme so as to perform data communication.
FIG. 1 illustrates application of gray mapping in which 4 bits are mapped to 16 signal points in such a way that the Hamming distance between bit sequences of adjacent signal points is 1. A transmitting side divides data that has been subjected to error correction coding by a coding device 11 into 4-bit segments, calculates a corresponding signal point through a gray mapping device 12, and transmits a transmission signal. A receiving side selects, from a reception signal, a signal point closest to the calculated signal point in terms of the Euclidean distance and performs, using a decoding device 14, decoding of the error correction code for a bit string obtained through a demapping device 13 that leads to 4 bits corresponding to the selected signal point.
However, a case may occur where the signal point selected by the receiving side differs from the transmitted signal point due to communication channel noise. In this case, a bit error occurs as a result of the demapping. A main factor of the occurrence of the error in a communication system is thermal noise whose amplitude obeys normal distribution, and a signal point which is closer to the transmitted signal point in terms of the Euclidean distance has a higher probability of being selected by the receiving side. Therefore, in a case where the Hamming distance between adjacent signal points that are likely to be erroneously selected due to the thermal noise is large, bit error rate with respect to the same noise level becomes higher. The gray mapping in which the Humming distance between all the adjacent signal points is 1 is an optimum scheme in this sense. However, from a viewpoint of effective application of the error correction code, it is not always necessary that the error correction coding is evenly applied to all the 4 bits that have been mapped to the signal point but the same effect may be obtained by applying the error correction coding to only a part of the 4 bits.
FIG. 2 illustrates a data communication scheme in which 4-bit mapping to the 16 signal points of the 16 QAM is modified. That is, in this scheme, error correction code is applied only to the lower 2 bits.
In this bit mapping, although the Hamming distance between the adjacent signal points is not necessarily 1, the Hamming distance between the adjacent signal points is 1 in terms of only the lower 2 bits, and the Euclidean distance between the signal points at which the lower 2-bit portions assigned thereto coincide with each other is largest.
On a transmitting side, the coding device 21 assigns a bit string that has been subjected to the error correction coding to the lower 2 bits, calculates the corresponding signal point through a double gray mapping device 22 as illustrated in FIG. 2, and transmits a transmission signal. On a receiving side, a first demapping device 23 selects, from a reception signal, a signal point closest to the calculated signal point in terms of the Euclidean distance and a decoding device 24 performs decoding of the error correction code for the lower 2 bits of the 4 bits corresponding to the selected signal point. Subsequently, a second demapping device 25 is used to select, from four signal points at which the 2 bits obtained through the error correction coding and the lower 2-bit portions assigned thereto coincide with each other, one that is closest to the received signal point in terms of the Euclidean distance so as to determine the undetermined upper 2 bits.
Due to the nature that the signal point which is closer to the transmitted signal point in terms of the Euclidean distance has a higher probability of being selected by the receiving side under the condition that the lower 2 bits are corrected properly through the error correction coding and the fact that the Euclidean distance between the signal points at which the lower 2-bit portions assigned thereto coincide with each other is large, a probability that error occurs in the upper 2 bits becomes significantly low. Thus, it can be said that absence of error correction coding for the upper 2 bits produces substantially no disadvantage. In particular, in a communication channel an increase in the bandwidth of which is limited due to the application of the error correction coding, an equivalent error rate can be achieved with a smaller number of the redundant bits as compared to the method illustrated in FIG. 1, which is very effective. The method of FIG. 2 can be said to one in which the bit mapping is devised to divide the 4 bits corresponding to each of the signal points into a bit portion for which the bit error probability is low and the remaining bit portion for which the bit error probability is high so as to apply the error correction coding to only the bit portion for which the bit error probability is high.
The example of the mapping method illustrated in FIG. 2 is called “double gray mapping” (NPL 3). This method, which applies the gray mapping independently to the upper bit portion to which the error correction coding is not applied and the lower bit portion to which the error correction coding is applied, can be applied to a case where the signal constellation is rectangular but cannot be applied to a 22n+1 QAM modulation and demodulation scheme in which the index is odd or a case (NPL 4) where the signal constellation is not rectangular even if the index is even.
Further, also in the gray mapping exemplified in FIG. 1 in which a non-encoded portion is not included but the error correction code is applied to all the bits, in the case where the signal constellation is not rectangular, it is not possible to make the Hamming distance between the bit sequences assigned to the adjacent signal points be 1 in general. With regard to a case where the signal constellation is cross-shaped in the 22n+1 QAM in which the index is odd, the method of PTL 1 is known as a mapping method in which the Hamming distance between the adjacent signal points becomes minimum.
Set partitioning is known as a bit mapping method for the signal constellations in different shapes, and a TCM scheme (NPL 2) that encodes the lower bit portion with a trellis code is known as the set partitioning approach. In the set partitioning approach, although the Euclidean distance between the signal points at which the lower bit portions assigned thereto which is to be subjected to encoding coincide with each other is maximum, an average Hamming distance between the adjacent signal points is not taken into consideration, so that the bit error rate of the lower bit portion is high. It follows that this set partitioning can be said to be a mapping method that is inadequate for application to error correction code (e.g, RS code or LDPC code) other than the trellis code supporting the set partitioning applied.